X₃₅₁₈

EULER LINE INTERCEPT OF LINE X₅₁X_54

X₃₅₁₈ = X₁₁₇₉-Ceva conjugate of X₄

5, 6, 7 3, 4, 5 Kepler Kimberling

X₃₅₁₈ (EULER LINE INTERCEPT OF LINE X₅₁X_54) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 3} (Euler line), {51, 54}

• Related Centers: X₃₅₁₉ (ISOGONAL CONJUGATE OF X₃₅₁₈), X₂ (CENTROID), X₃ (CIRCUMCENTER), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₅₄ (KOSNITA POINT)

Trilinears: \(4 \cos A - 3 \sec A : :\)

Barycentrics: \(a^{2} (a^{4} + b^{4} + c^{4} - 2 a^{2} b^{2} - 2 a^{2} c^{2} - b^{2} c^{2})/(a^{2} - b^{2} - c^{2}) : :\)

Search Value (6, 9, 13): \(0.338108597674\)

▸ Incident Central Lines18 lines

{2, 3}, {49, 143}, {51, 54}, {52, 110}, {53, 1601}, {93, 324}, {98, 3456}, {107, 1141}, {112, 3199}, {156, 568}, {184, 1199}, {389, 1495}, {575, 1843}, {576, 1974}, {1112, 3043}, {1147, 3060}, {1304, 3470}, {1866, 1870}

▸ Functional Relations11 relations

• X₃₅₁₈ = isogonal conjugate of X₃₅₁₉

• X₃₅₁₈ = anticomplement of X₃₇₄₅₂

• X₃₅₁₈ = circumcircle-inverse of X₃₇₉₄₃

• X₃₅₁₈ = X₁₁₇₉-Ceva conjugate of X₄

• X₃₅₁₈ = X₂₉₆₅-cross conjugate of X₁₉₉₄

• X₃₅₁₈ = crosspoint of X₃₄₄₂ and X₃₄₄₃

• X₃₅₁₈ = crosssum of X₆₃₃ and X₆₃₄

• X₃₅₁₈ = X₃-isoconjugate of X₂₉₆₂

• X₃₅₁₈ = {X₄,X₂₄}-harmonic conjugate of X₁₈₆

• X₃₅₁₈ = perspector of ABC and orthocentroidal-of-orthic triangle

• X₃₅₁₈ = crosssum of X₁₄₈₁₃ and X₁₄₈₁₄

Notes

As a point on the Euler line, X₃₅₁₈ has Shinagawa coefficients \((4F, -3E - 4F)\).